受简谐激励弹簧测力机构的1/3次亚谐共振研究  

STUDY ON 1/3 SUBHARMONIC RESONANCE OF A DYNAMOMETER SUBJECT TO HARMONIC EXCITATION

作　　者：杨志安[1] 程英辉[2] 

机构地区：[1]唐山学院唐山市结构与振动工程实验室,唐山063000 [2]河北理工大学机械工程学院,唐山063000

出　　处：《振动与冲击》2006年第6期84-87,91,共5页Journal of Vibration and Shock

摘　　要：为研究弹簧测力机构的1/3次亚谐共振问题,应用拉格朗日方程得到有阻尼弹簧测力机构在简谐激励作用下具有周期系数的非线性运动微分方程-Duffing-M ath ieu方程;根据非线性振动的多尺度法求得系统满足1/3次亚谐共振情况的一次近似解,并对其进行数值计算。分析了激力、谐调值、阻尼、弹簧刚度等对系统的影响。随着阻尼的增加,系统幅频响应曲线向开口方向移动。随着弹簧刚度和激力的增大,系统幅频响应曲线上下两条曲线的距离逐渐增大。对于硬刚度系统,当谐调值大于零时,随着谐调值的增大,系统幅频响应曲线幅值逐渐增大。对于软刚度系统,当谐调值小于零时,随着谐调值的减小,系统幅频响应曲线幅值逐渐增大。In order to investigate 1/3 subharmonic resonance of a dynamometer,the nonlinear mathematical model of a dynamometer subject to harmonic excitations is established by means of Lagrange equation.It is a Duffing-Mathieu equation.By using the method of multiple scales for nonlinear vibration analysis,the first approximation solution of subharmonic resonance of the system is obtained.Numerical analysis for the influence of excitation,tuning,damping and stiffness on the system is carried out.With increasing in damping,the amplitude-frequency curves of the system their opening mouth.With increasing in stiffness and excitation force,the distance between amplitude-frequency curves of the system enlarges.For hard stiffness system,the amplitude of amplitude-frequency curves of the system enlarges with tuning value rising.For soft stiffness system,the amplitude of amplitude-frequency curves of the system enlarges with tuning value dropping.

关 键 词：拉格朗日方程 测力机构 多尺度法 亚谐共振 

分 类 号：O321[理学—一般力学与力学基础]